Stirling Council's four Conservative members have described themselves as "key" to the future direction of the local authority.
A final decision on the future of the council will be made by 13 March
The comments came after the SNP's seven council members tabled a motion of no confidence in the ruling administration.
No one party has enough members for an outright majority to run the council.
However, since May a coalition of eight Labour members and three Liberal Democrats have ruled the authority.
The Nationalists said the motion was in response to a lack of progress since the Labour/Lib Dem administration took control.
Deputy Conservative group leader Cllr Neil Benny said his party were yet to reveal who they would back.
He said: "Our primary consideration is what is best for Stirling.
"On 13 March we will take a view as to whether Stirling Council needs new leadership and who will best deliver for the people of Stirling.
"We are proud to have delivered a modest tax cut to the hard-pressed Stirling taxpayer, but we are also aware of the need for leadership and there are some tough choices ahead."
Since the motion was tabled on Friday, members have until 13 March to hold a vote to determine who will lead the next administration.
A spokesman for the council said: "The clerk to the council is consulting all four party group leaders and the provost about the date for the special meeting.
"By law, it must be held within 14 days of receipt of the requisition, i.e. not later than 13 March."